Kyoto Journal of Mathematics

Special values of the Hurwitz zeta function via generalized Cauchy variables

Takahiko Fujita and Yuko Yano

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As a continuation of the work of Bourgade, Fujita, and Yor, we show how to recover the extension of the Euler formulae concerning some special values of the Hurwitz zeta function from the product of two, and then N, independent generalized Cauchy variables. Meanwhile, we consider the ratio of two independent generalized Cauchy variables and give another proof of the partial fraction expansion of the cotangent function.

Article information

Kyoto J. Math., Volume 52, Number 3 (2012), 465-477.

First available in Project Euclid: 26 July 2012

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Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory
Secondary: 60G52: Stable processes 11M35: Hurwitz and Lerch zeta functions


Fujita, Takahiko; Yano, Yuko. Special values of the Hurwitz zeta function via generalized Cauchy variables. Kyoto J. Math. 52 (2012), no. 3, 465--477. doi:10.1215/21562261-1625163.

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